I'm trying to figure out if a logical error was committed here or not. Can a logician help me out?

Reply to Need Logic Help

A lot will depend on whether you think it beneficial to involve a logic of belief. If not, or else at least to help decide, let's make the parallel as clear as possible:

P1: All logics that are objective are cared about by X
P2: Logic Y is not cared about by X
C: Logic Y is not objective

P3: All men that are Supermen are believed by Lois Lane to fly
P4: Man Clark Kent is not believed by Lois Lane to fly
C: Man Clark Kent is not a Superman

In both cases, there's no logical error except perhaps a choice-of-logic error: you might decide you must affirm both premises yet reject the conclusion. Because for example you are too polite to question P1/P3. Then you're gonna need a bigger (and more controversial) logic. But questioning P1/P3 is simpler.

Quoting Need Logic Help

the issue is that maybe Y really is part of objective logic but X doesn’t know it.

And the simplest way to make that point is just to say that P1 fails. "There are more objective logics in heaven and earth than are cared about in X's philosophy." No need to get modal on his ass, and call it a (necessarily exotic) logical error, rather than a (simple) factual one.

Quoting Need Logic Help

“P1: X cares about objective logic, P2: X does not care about Y, C: Y is not included in objective logic”

How about this

T Clark likes fruit. T Clark does not like apples. Therefore apples are not fruit.

I guess the question is - does the statement "T Clark likes fruit," mean that he has to like all fruit or just fruit in general.

Reply to bongo fury

Just to be clear, I'm not out to get Matt Dillahunty or anything. I genuinely just want to know the truth of the matter.

So does P1 fail or does it not? If it fails, why? If not, why not?

If P1/P2 are correct in what you laid out, then does C follow? If not, doesn't there need to be some error of logic?

And if P3/P4 are correct in what you laid out, then does C follow? If not, doesn't there need to be some error of logic?

Reply to T Clark

That's a good point. How do you think that the first premise could be more clearly stated?

Quoting Need Logic Help

That's a good point. How do you think that the first premise could be more clearly stated?

X cares about every aspect of objective logic.

I think the problem here is that the statements are being made in everyday English. When I say "I like fruit," it doesn't necessarily mean I like absolutely all fruit. I really like green vegetables - brussel sprouts, cabbage, lettuce, green beans, lime beans, spinach, cauliflower, broccoli. I don't like okra or broccoli rab. Those are both perfectly reasonable statements for me to make.

Reply to T Clark

What if you say you like fruit, but then say that you don't like tomatoes, and then conclude that a tomato isn't a fruit? A tomato is in fact a fruit, apparently.

Reply to T Clark

I guess that we need to know exactly what argument Matt was presenting. Right? Or else we can't evaluate if it's logically solid or not logically solid.

Reply to T Clark

What if you say that you like ALL fruit, I mean, and not tomatoes, and then find out that tomatoes are fruit.

Quoting Need Logic Help

Dillahunty makes a logical error here because he presents the argument “P1: X cares about objective logic, P2: X does not care about Y, C: Y is not included in objective logic”, but imagine the argument “P3: Lois Lane believes Superman can fly, P4: Lois Lane does not believe Clark Kent can fly, C: Clark Kent is not Superman”—the issue is that maybe Y really is part of objective logic but X doesn’t know it.

Dillahunty's argument
P1: All things X cares about are things that are logically objective
P2: No things X cares about are things identical to Y
Ergo,
C. No things that are logically objective are things identical to Y

Tests for validity of Dillahunty's argument:
1. Distributed middle term test: Passed
2. Distributed conclusion test: Fail. The category "things that are logically objective", distributed in the conclusion, isn't distributed in the premises. It should be if the argument is to be valid.

Dillahunty's argument is invalid.

Reply to TheMadFool

Thanks! This is interesting. Curious to see what the other users in this thread think of your breakdown!

Can you explain the two tests that you performed?

Quoting Need Logic Help

So does P1 fail or does it not? If it fails, why?

Because,

Quoting bongo fury

"There are more objective logics in heaven and earth than are cared about in X's philosophy."

Quoting Need Logic Help

If not, why not?

Because all of them are cared about by X.

Quoting Need Logic Help

If P1/P2 are correct in what you laid out,

Assuming you mean, if they are a fair presentation of the premises actually being asserted,

Quoting Need Logic Help

then does C follow?

Sure.

Quoting Need Logic Help

If not,

I take it you mean, if they are the actual premises being asserted, but C doesn't follow,

Quoting Need Logic Help

doesn't there need to be some error of logic?

Yes. But there isn't. C follows, unless you want to get bogged down in a bigger and more controversial logic (one of belief). I've presented the premises in such a way that you can dispute them, rather than the logic.

Quoting Need Logic Help

And if P3/P4 are correct in what you laid out, then does C follow? If not, doesn't there need to be some error of logic?

Likewise.

Quoting Need Logic Help

Thanks! This is interesting. Curious to see what the other users in this thread think of your breakdown!

Can you explain the two tests that you performed?

Quoting TheMadFool

Dillahunty's argument
P1: All things X cares about are things that are logically objective
P2: No things X cares about are things identical to Y
Ergo,
C. No things that are logically objective are things identical to Y

Tests for validity of Dillahunty's argument:
1. Distributed middle term test: Passed
2. Distributed conclusion test: Fail. The category "things that are logically objective", distributed in the conclusion, isn't distributed in the premises. It should be if the argument is to be valid.

Dillahunty's argument is invalid.

Distributed middle term test: The middle term, the term missing in the conclusion ,the inferential link between the major and minor terms in the conclusion, must be distributed i.e. there must be a premise that makes a statement about ALL members of the middle term. In Dillahunty's argument, the middle terms is "all things X cares about" and it's distributed premise 1 (P1).

Distributed conclusion test: Every term distributed in the conclusion must be distributed at least once in the premises. The term "things that are logically objective" is distributed in the conclusion but it isn't in any of the premises. Ergo, Dillahunty's argument is invalid.

That's all there is to it.

Reply to TheMadFool

Thanks! Are these two tests commonly performed in logic?

Would every logician agree that these tests are solid ones to perform, or would there be any contention on that?

Reply to Need Logic Help I don't see an error (though I have not watched the video).

If it is true that Tom cares about all objective truths, and also true that Tom does not care about Y, then we can conclude that Y is not an objective truth.

If all As are Bs (if all objective truths are cared for by Tom), and C is not a B, then C is not an A.

The superman example is different. Lane believes Superman can fly. Lane does not believe Clark Kent can fly. Ok. What follows from that is not that superman isn't Clark Kent, but that Lane believes Superman can fly and believes that Clark Kent can't.
1.p
2.q
3. Therefore p and q.

Of course, as those beliefs are about one and the same person, they can't both be true. But that's a different point.

So I think the youtube commentator doesn't know what he's talking about and has compared dilahunty's argument to a quite different and obviously invalid one.

Reply to Bartricks

Thanks for replying!

Superman is in the category of people who Lois believes can fly.

Clark Kent isn't.

Therefore, Clark Kent isn't Superman.

Reply to Need Logic Help Yes, if those premises are true, that follows.
Those premises are not equivalent to these, however:
1. Lane believes Kent can't fly
2. Lane believes Superman can fly

Note: Clark Kent is in the class of people Lane believes can fly (because he is superman and the person of superman is in the class of people she believes can fly), she just doesn't realize this.

This is valid:

1. Kent can't fly
2. Superman can fly
3. Therefore kent isn't Superman

This isn't

1. Lane believes Kent can't fly
2. Lane believes Superman can fly
3. Therefore Kent isn't superman

This is:

1. Lane believes Kent can't fly
2. Lane believes superman can fly
3. Therefore lane believes Kent can't fly and believes superman can fly

If - if - Dilahunty made this argument:

1. If P then Q
2. Not Q
3. Therefore not P

Then his argument was valid. And it sounds as if he did.(if x is an objective truth, then I will care about it; I don't care about it; therefore it is not an objective truth).

Quoting Need Logic Help

What if you say that you like ALL fruit, I mean, and not tomatoes, and then find out that tomatoes are fruit.

You're making this a lot more difficult than it needs to be. Logic is supposed to be a tool to help find the truth, not a game to find the most obscure, trivial, and convoluted examples possible.

This is from Wikipedia:

[i]A fallacy of division is an informal fallacy that occurs when one reasons that something that is true for a whole must also be true of all or some of its parts.

An example:

• The second grade in Jefferson elementary eats a lot of ice cream
• Carlos is a second-grader in Jefferson elementary
• Therefore, Carlos eats a lot of ice cream

[/i]

Reply to T Clark

And how exactly does the fallacy of division apply to Matt's argument?

Why isn't Bartricks correct that Matt didn't commit any error?

Quoting Need Logic Help

I guess that we need to know exactly what argument Matt was presenting. Right?

And there may be no incontrovertible fact about this matter. But you'd have to be disingenuous or mad to think that P1 was best formulated as,

Quoting TheMadFool

P1: All things X cares about are things that are logically objective

rather than the other way round. That way, of course the whole argument is invalid. And you wouldn't need any medievalisms (about distributed middles) to show it. Just use a Venn diagram.

Whereas actually,

Quoting bongo fury

C follows, unless you want to get bogged down in a bigger and more controversial logic (one of belief).

Or unless you have chosen a bizarre and foolish presentation of P1. Then you are bogged down in a spurious and inexplicable representation of what was said. Which is no better than a spurious injection of modal logic.



Quoting Bartricks

If it is true that Tom cares about all objective truths, and also true that Tom does not care about Y, then we can conclude that Y is not an objective truth.

Yes.

Quoting Bartricks

If - if - Dilahunty made this argument:

1. If P then Q
2. Not Q
3. Therefore not P

Then his argument was valid.

Yes, and he probably did. See above.



Quoting Bartricks

The superman example is different.

Please not. You're inviting the enthusiasts for modal logic to show off, and end up perpetuating the silly libel of a logical error.



Quoting TheMadFool

thinking in the same way as Aristotle (roughly 2 millennia ago) and Gottlob Frege (approximately a century ago). That's like going to a modern pharmacy with a prescription made out by none other than Hippocrates

No, it's like knowing what you're talking about.

Quoting bongo fury

No, it's like knowing what you're talking about.

I don't deny the exceptional utility of classical logics and its spinoffs (Aristotle, Frege, Peirce, et al) but, seriously, they fail to capture some of the nuances and subtleties of nature, no? What's up with so-called temporal logic, fuzzy logic, paraconsistent logic, multi-valued logic, etc? Nobody in faer right mind would've taken the trouble to invent them if traditional two-valued predicate logic could handle the complexities inherent to thinking about reality. Just saying...

Quoting Need Logic Help

And how exactly does the fallacy of division apply to Matt's argument?

I think I've laid out my argument pretty clearly. I'll leave it at that.

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